Open Access

Weak convergence of an iterative sequence for accretive operators in Banach spaces

Fixed Point Theory and Applications20062006:35390

DOI: 10.1155/FPTA/2006/35390

Received: 21 November 2005

Accepted: 6 December 2005

Published: 8 June 2006

Abstract

Let be a nonempty closed convex subset of a smooth Banach space and let be an accretive operator of into . We first introduce the problem of finding a point such that where is the duality mapping of . Next we study a weak convergence theorem for accretive operators in Banach spaces. This theorem extends the result by Gol'shteĭn and Tret'yakov in the Euclidean space to a Banach space. And using our theorem, we consider the problem of finding a fixed point of a strictly pseudocontractive mapping in a Banach space and so on.

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Authors’ Affiliations

(1)
Department of Economics, Chiba University
(2)
Department of Mathematical and Computing Sciences, Tokyo Institute of Technology

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Copyright

© Koji Aoyama et al. 2006

This article is published under license to BioMed Central Ltd. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.